
This approximation corresponds to ignoring higher-loop radiative corrections and is appropriate for fields that varies slowly with time [1]}. Finally, the equation of motion of the Wigner function is given by [2]}
\(i\hbar D_t W(\mathbf {r},\mathbf {p}) =m \left[ \beta  , W \right]+ \left[ \tilde{\textbf {p}}\cdot \mathbf {\alpha } , W \right]-\frac{i\hbar }{2} \left\lbrace  \textbf {D}, W \right\rbrace ,\) 
